Algorithm for sampling from the residuals

1: Sample ηijk independently from a standard Normal distribution, assuming no missing data;

2: Compute εijk using the AR(1) model, imputing the values ηijk as residuals;

3: Compute yijk using the model (3), imputing εijk as residuals;

4: Determine the missing data for each biomarker with the following sampling procedure: Sample from a 2 state (not available (NA), not NA) non-homogeneous Markov chain indexed by the successive visits. The transition matrix was estimated separately for each status at baseline (N, MCI and AD) and before hand.

5: Estimate all the parameters from the simulated dataset with missing data obtained at the last step using Alg. 1. Notate $c_k^{(m)}$ the estimated parameter c for biomarker k at iteration m.